A standard local density approximation and its self-interaction corrected version are applied to study spontaneous magnetization, promoted by localized p electron holes, of polar oxygen-terminated ZnO surfaces. The electronic properties and magnetic exchange interactions of three different facets are calculated. It is demonstrated that partially filled oxygen p orbitals of the polar surfaces exhibit magnetic moment formation and long range magnetic order leading to the occurrence of a ferromagnetic ground state. Monte Carlo simulations predict Curie temperatures above room temperature. In contrast to isolated defects in bulk materials, applying correlation corrections to the localized p-like surface states does not lead to a collapse of magnetic interaction: as the weakening of the magnetic interaction, caused by the reduced electronic overlap, is compensated by a strengthening due to an increase of the magnetic moments, the ferromagnetism can principally persist above room temperature, provided a large hole concentration exists.